Power Transfer Through Strongly Coupled Resonances by Andr6 Kurs Submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Master of Science in Physics at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2007 @ Massachusetts Institute of Technology 2007. All rights reserved. /I A uthor ............. ................. ............. Department of Physics August 10, 2007 Certified by............... .•V ................... ...... .. .. I Marin Soljaui6 Assistant Professor of Physics Thesis Supervisor Accepted by Thomas J. Gretk Associate Department Head for Education MASSACHUSETTS INST[UTE OF TECHNOLOGY LIBRARIES ARCHIVES i J ..... Power Transfer Through Strongly Coupled Resonances by Andre Kurs Submitted to the Department of Physics on August 10, 2007, in partial fulfillment of the requirements for the degree of Master of Science in Physics Abstract Using self-resonant coils in a strongly coupled regime, we experimentally demonstrate efficient non-radiative power transfer over distances of up to eight times the radius of the coils. We use this system to transfer 60W with approximately 45% efficiency over distances in excess of two meters. We present a quantitative model describing the power transfer which matches the experimental results to within 5%, and perform a finite element analysis of the objects used. We finally discuss the robustness of the mechanism proposed and consider safety and interference concerns. Thesis Supervisor: Marin Soljaaid Title: Assistant Professor of Physics Acknowledgments I would like to thank all my collaborators on this project: Aristeidis Karalis, Robert Moffatt, Prof. John D. Joannopoulos, Prof. Peter Fisher, and Prof. Marin Soljadid. It has been a pleasure to work with all them. I would like to doubly thank my advisor, Marin Soljadid, for letting me work on this project, for all his support, and for his help in the laboratory during the final stretch of measurements. My thanks also go to Mike Grossman for his help with machining, Ivan Celanovid for helping with the electronics, Zheng Wang for his assistance with COMSOL, and to Mark Rudner for useful discussions. Contents 1 Introduction 2 Theory of strongly coupled systems 2.1 Motivation and basics ........ ..... 2.2 Single oscillator driven at constant frequency . 2.3 Two coupled oscillators . ... ... .... .. 2.4 Transferring power ............... 3 Analytical model for self-resonant coils 19 3.1 Description of self-resonant coils . .... .............. 19 3.2 Assumptions of the analytical model . .. .............. 20 3.3 Resonant frequency .. ... .. .. ... .............. 20 3.4 Losses .. ..... ..... ..... ... ............... 2 1 3.5 Coupling coefficient between two coils .. .............. 22 3.6 Validity of the quasi-static approximation .............. 23 4 Finite element analysis of the resonators 4.1 O verview .................................. 4.2 A single isolated coil ........................... 4.3 Two coupled coils ............................. 5 Comparison of theory with experimental parameters 5.1 Frequency and quality factor ....................... 5.2 Coupling coefficient ............................ 5.3 Range of the strong coupling regime . ....... ........... 6 Measurement of the efficiency 34 6.1 Description of the setup ....................... 34 6.2 Results .... ......... ...... .... .... ..... ... 34 7 Practical issues 37 7.1 Robustness of the strong coupling regime . ............... 37 7.2 Safety and interference concerns ................... .. 39 7.3 Directions for future research ...................... 40 List of Figures 2-1 Efficiency as a function of the parameter K/NV/rSrD. In the vicinity of K/J/PSID ý- 1, the efficiency rises sharply, thus justifying the cri- terion ./ P/SD > 1 for efficient power transfer.The efficiency curve asymptotes to 1 as Is/V -- oo. .................. 18 4-1 Lowest eigenmode of a self-resonant coil, simulated with COMSOL Multiphysics. The colormap represents the z-component of the mag- netic field ................... .. ............. 25 4-2 Even (left) and odd eigenmodes of two coupled self-resonant coils. The colormap represents the z-component of the magnetic field. ........ 26 5-1 Experimental setup for measuring Q. The self-resonant coil is the cop- per wire wrapped around the piece of pink styrofoam. The excitation coil to its right is connected to a function generator, while the pickup coil on the opposite side is connected to the oscilloscope. ........ 29 5-2 Experimental setup for measuring ti. The self-resonant coil on the right-hand side is driven by a coil connected to a function generator. A pickup coil measures the amplitude of the excitation in the second coil. ................... ............... .. 30 5-3 Comparison of experimental and theoretical values for , as a function of the separation between coaxially aligned source and device coils (the wireless power transfer distance). Note that when the distance D between the centers of the coils is much larger than their characteristic size, K scales with the D - 3 dependence characteristic of dipole-dipole coupling ... ... .... .... .... .. .... .... .... 31 5-4 Theoretical and experimental r. as a function of distance when one of the coils is rotated by 45% with respect to coaxial alignment...... 31 5-5 Theoretical and experimental K as a function of distance when the coils are coplanar. ............................... 32 5-6 Comparison of experimental and theoretical values for the parameter 1/F as a function of the wireless power transfer distance. The theory values are obtained by using the theoretical . and the experimentally measured F. The shaded area represents the spread in the theoretical I/F due to the ±5% uncertainty in Q. ................. 33 6-1 Schematic of the experimental setup. A is a single copper loop of radius 25cm that is part of the driving circuit, which outputs a sine wave with frequency 9.9MHz. S and D are respectively the source and device coils referred to in the text. B is a loop of wire attached to the load ("light-bulb"). The various K's represent direct couplings between the objects indicated by the arrows. The angle between coil D and the loop A is adjusted to ensure that their direct coupling is zero, while coils S and D are aligned coaxially. The direct couplings between B and A and between B and S are negligible. ............ 35 6-2 Comparison of experimental and theoretical efficiencies as functions of the wireless power transfer distance. The shaded area represents the theoretical prediction for maximum efficiency, and is obtained by inserting the theoretical values from Fig. 5-6 into Eq. 2.12 (with w/ = v/1 + 2/F 2 .) The black dots are the maximum efficiency obtained from Eq. 2.12 and the experimental values of K/F from Fig. 5-6. The red dots present the directly measured efficiency, as described in the text. ................................ 35 7-1 60W light-bulb being lit from 2m away. Note the obstruction in the lower im age ..... .... ..... ..... .. .. ..... ..... 38 List of Tables 7.1 Effect of replacing self-resonant coils with capacitively-loaded loops and of lowering the resonant frequency on electromagnetic fields 20cm away from the surface of the device loop. The power radiated by the system is also shown. The total power transferred is 60W. ...... 39 Chapter 1 Introduction At the turn of the 20th century, Nikola Tesla [1, 2, 3] devoted much effort to developing a system for transferring large amounts of power over continental distances. His main goal was to bypass the electrical-wire grid, but for a number of technical and finan- cial difficulties, this project was never completed. Moreover, typical embodiments of Tesla's power transfer scheme (e.g., Tesla coils) involve extremely large electric fields and are potential safety hazards. The past decade has witnessed a dramatic surge in the use of autonomous electronic devices (laptops, cell-phones, robots, PDAs, etc) whose batteries need to be constantly recharged. As a consequence, interest in wirelessly recharging or powering such devices has reemerged [4, 5, 6]. Our attempts to help to fulfill this need led us to look for physical phenomena that would enable a source and a device to exchange energy efficiently over mid-range distances, while dissipating relatively little energy in extraneous objects. By mid-range, we mean that the separation between the two objects effecting the transfer should be of the order of a few times the characteristic sizes of the objects. Thus, for example, one source could be used to power or recharge all portable devices within an average-sized room. A natural candidate for wirelessly transferring powering over mid-range or longer distances would be to use electromagnetic radiation. But radiative transfer [7], while perfectly suitable for transferring information, poses a number of difficulties for power transfer applications: the efficiency of power transfer is very low if the radiation is omnidirectional (since the power captured is proportional to the cross-section of the receiving antenna, and most of the power is radiated in other directions), and requires an uninterrupted line of sight and sophisticated tracking mechanisms if radiation is unidirectional (which might also damage anything that interrupts the line of sight). An alternative approach, which we pursue here, is to exploit some near-field in- teraction between the source and the device, and somehow tune this system so that efficient power transfer is possible. A recent theoretical paper